In [1]}, it was shown that the range of solvability in \(L^p\)  of the Dirichlet problem for these operators could be extended to
the full range of \(1<p<\infty \)  if the Carleson norm of the matrix coefficients was sufficiently small.
Operators whose coefficients satisfy this small Carleson norm condition also arise naturally. For example, consider the Laplacian in the region above a graph \(t = \varphi (x)\) .
If the function \(\varphi \)  has the property that \(\nabla \varphi \in L^{\infty } \bigcap \)  VMO, a weaker property than \(\varphi \in C^1\) , the solvability of the Dirichlet problem in \(L^p\)  for \(1 < p < \infty \)  is a corollary of the main theorem of [1]}
via a change of variable. The function space \(VMO\) , introduced by Sarason ([3]}) consists of those \(BMO\)  (bounded mean oscillation) functions that can be approximated in \(BMO\)  norm by \(C^\infty \)  functions.
